In a medium bowl whip egg yolks for 1 minute with a hand mixer on medium, until bright yellow. Add ¾ cup sugar, salt, and 1 teaspoon nutmeg, whip for 1 minute.
Turn on the heat to medium in a large pot add half and half, cream and remaining nutmeg, bring to a slight boil, about 3 minutes. Stir in ¼ cup of warm liquid into the egg mixture. Pour back into the pot, cook for 3 minutes on medium, until the eggnog coats the back of a spoon. Stir in vanilla extract and ½ cup rum. Remove from heat and cool for 10 minutes.
Place eggnog in a freezer safe bowl, place in the freezer for 3-4 hours, until slushy forms.
In a large bowl whip egg whites with a hand mixer on medium for 2 minutes, until stiff peaks form. Slowly add ¼ cup of sugar, 1 tablespoon spiced rum and whip for 2 minutes.
In a blender add 1 cup crushed ice and half the slushy eggnog mixture, blitz on high for 1 minute. Repeat. Divide evenly amongst 4 glasses, make sure to get some of the foam, and garnish with a sprinkle of nutmeg.